The one-parameter scaling theory of localization describes the behavior of disordered systems in integer dimensions. We test its limits for systems with non-integer dimensions by studying conduction on fractal lattices with disorder. Notably, we demonstrate a new effect for symplectic Hamiltonians living on certain fractal families with Hausdorff dimension lower than two. Analytical arguments and numerical simulations show that weak antilocalization corrections induce an attractive critical point with a scale-invariant conductance. This phenomenon is not seen in integer dimension lattices, which have at most a single repulsive critical point, marking the metal-insulator transition.